Reduce to lowest terms: $- \dfrac{5}{9} \div \dfrac{6}{5} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{6}{5}$ is $ \dfrac{5}{6}$ Therefore: $ - \dfrac{5}{9} \div \dfrac{6}{5} = - \dfrac{5}{9} \times \dfrac{5}{6} $ $ \phantom{- \dfrac{5}{9} \times \dfrac{5}{6}} = \dfrac{-5 \times 5}{9 \times 6} $ $ \phantom{- \dfrac{5}{9} \times \dfrac{5}{6}} = \dfrac{-25}{54} $